Hungry lions and lamb is a classic game theory problem. It goes like this: there is a group of hungry lions on an island covered with plenty of grass and no other animals in sight. The lions are perfectly rational, which means survival is their priority, and each knows the others are rational too. The former suggests they prefer hunger over death, and the latter implies they don’t try to outsmart each other.
One day, a lamb appears from nowhere. The lamb is just big enough to become a meal for one lion. And the lion that eats the lamb becomes too full to defend itself against another hungry lion. Given these situations, what is the survival probability for the lamb?
Let’s arrange the lamb and the lions as follows. Consider the simplest case of one lamb and one lion.
Since there are no other lions around, there is no threat for the lion to eat the lamb. What happens if there are two lions?
The situation is different here: lion2 is ready to eat lion1 if the latter chooses to eat the lamb. So, lion 1, being rational, controls the impulse and spares the lamb. The lamb survives. What about three lions?
The lion3 is ready to eat lion2 if the latter becomes full. Knowing this reasoning, lion2 will spare lion1. Since the lion1 knows that, it will eat the lamb.
To conclude: if there are an odd number of lions in the pride, the first lion can eat the lamb without worrying about being eaten by other lions. If the number is even, the lamb will be spared.
